Transcript Statistics of Experimental Design

Statistics of Experimental Design
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Ludolf E. Meester, Statistics Dept.
Peter J.T. Verheijen, Chemical Eng. Dept.
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Aim
• Introduction probability and statistics
• Familiarise engineering students with the
jargon of the statisticians
• Model-based analysis of experimental data
• Design of experiments
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Contents
Probability
Distributions
Example 1:
Probability of success in test
Descriptive Statistics
Estimation theory
Example 2:
Probability of success in test 2
given that test 1<5.5?
Hypothesis testing
Linear Model
Non-linear regression
Answer: 0.55 and 0.15
Design of experiment
Model selection/discrimination
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Contents
Probability
Distributions
0.35
mu=5.72
sigma=1.55
0.3
Descriptive Statistics
0.25
Density
Estimation theory
Hypothesis testing
0.2
0.15
Linear Model
0.1
Non-linear regression
0.05
Design of experiment
0
0
Model selection/discrimination
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2
3
4
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Score
6
7
8
9
10
5
Contents
Probability
25
Distributions
Test 1
5. 6
5. 1
6. 8
3. 4
6. 8
4. 6
5. 6
6. 3
5. 0
7. 6
5. 6
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Descriptive Statistics
Frequency
Estimation theory
Hypothesis testing
15
10
Linear Model
Non-linear regression
Test 2
6. 1
7. 5
6. 6
3. 1
8. 4
6. 4
4. 9
10. 0
4. 0
8. 2
5. 8
5
Design of experiment
0
Model selection/discrimination
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1
2
3
4
5 6
Score
7
8
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Contents
Descriptive Statistics
Probability
Distributions
Example:
What is mu and sigma?
Estimation theory
•Bias
•Robustness
•Confidence Interval
•Bootstrap methods
Hypothesis testing
Linear Model
Non-linear regression
Design of experiment
Model selection/discrimination
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Contents
Descriptive Statistics
Probability
Distributions
Estimation theory
Hypothesis testing
Linear Model
Non-linear regression
Example 1:
When you have less than 4. 5
on test 1, you will not pass
Example 2:
Average Test1=Average Test 2
Answer: No and no
Design of experiment
Model selection/discrimination
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Contents
Descriptive Statistics
10
Probability
9
8
Distributions
Estimation theory
Hypothesis testing
Score Test 2
7
6
5
4
Linear Model
Non-linear regression
3
2
1
Design of experiment
0
1
2
3
4
5
6
Score Test 1
7
8
9
10
Model selection/discrimination
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Contents
Descriptive Statistics
10
Probability
9
8
Distributions
Hypothesis testing
Linear Model
Non-linear regression
Score Test 2
Estimation theory
7
6
5
4
3
2
1
0
Design of experiment
0
1
2
3
4
5
6
Score Test 1
7
8
9
10
Model selection/discrimination
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Contents
Descriptive Statistics
Probability
Distributions
Estimation theory
Hypothesis testing
Linear Model
Non-linear regression
… To improve estimate
... To improve prediction of model
Design of experiment
Model selection/discrimination
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Contents
Descriptive Statistics
Probability
Given Data:
Choose between models
Distributions
Estimation theory
Hypothesis testing
Given Different Models:
Choose between experiments
Linear Model
Non-linear regression
Design of experiment
Model selection/discrimination
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The Lectures
1.
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3.
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Introduction, probability
Probability distributions
Simulation, expectation and variance
Joint distributions
Central limit theorem, data exploration
Estimation
Hypothesis testing
Stochastic vectors: linear model and estimation
Linear model, confidence interval and hypothesis testing
Linear model, Non-linear regression
Non-linear regression
Experimental design
Model selection
Review
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Overview
Entities
Data = Model + Experimental Error
Actions
Characterisation
Experimentation
Estimation
Hypothesis testing
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… to be continued
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Course Material and Information
•Part I: A Modern Introduction to Probability and
Statistics by Dekking et al, ISBN 1-85233-896-2;
(Autumn 2004 and later versions of Kanstat lecture notes still usable.)
•Part II: Lecture Notes, plus exercises
•Exercises and Examination Set Edition 7 available as PDF
Data for exercises and past examinations
•Software:
SSORstat
PastiFit
PastiMos
Excel
…. any other, eg Splus, SAS, SPSS, Matlab
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Where, what
VSSD
A Modern Introduction to Probability and Statistics by
Dekking et al, ISBN 1-85233-896-2
Computer rooms
Data for exercises and past examinations
Software: SSORstat, PastiFit, PastiMos and Excel
Web page: http://dutiosc.twi.tudelft.nl/~a90 (also via BB page)
Data for exercises and past examinations (zip-file)
Exercises and Examination Set (1994-2006) as pdf
Lecture notes Statistiek van Proefopzetten as pdf
Download software: SSORstat, PastiFit, PastiMos
And of course e-mail to the lecturers:
[email protected], [email protected]
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Course Material and Information
Changes with respect to 2005/2006
Lecture notes: Statistiek van proefopzetten ONLY available as
pdf on website.
Exercises and Examination Set: minor updates and inclusion of
exams 2004/2005; ONLY available as pdf on website.
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Timetable
• Course schedule 3rd period Room B
– Thursday: hour 1+2 Lectures (/Exercises)
– Friday: hour 5+6+7 Lectures/(Computer) Exercises
• Course schedule 4th period Room B
– Wednesday: hour 2+3+4 Lectures/(Computer) Exercises
– Thursday: hour 3+4 Lectures/Exercises
• Examination schedule
– Full course examination: Thu., June 14, 14-17
– Full course examination: Tue., August 28, 14-17
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Examination
Material present:
• Computer with
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SSORstat
PastiFit
PastiMos
Excel
• Formulas (from appendices Lecture Notes)
Allowed: normal calculator
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Examination
Percentage Geslaagd
Percentage voldoende
70%
60%
50%
40%
30%
20%
1988 1990 1992 1994 1996 1998 2000 2002 2004 2006
Jaar
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… and what else
Dans le domaine de la science, le hasard ne
favorise que les esprits qui ont été préparés.
Louis Pasteur, 1822-1895
…. or ‘’Chance favors the prepared mind!’’
…. or “Het toeval begunstigt de voorbereide geest’’
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